IDEAS home Printed from https://ideas.repec.org/p/zbw/dicedp/326.html
   My bibliography  Save this paper

Nonparametric estimation of the random coefficients model: An elastic net approach

Author

Listed:
  • Heiss, Florian
  • Hetzenecker, Stephan
  • Osterhaus, Maximilian

Abstract

This paper investigates and extends the computationally attractive nonparametric random coefficients estimator of Fox, Kim, Ryan, and Bajari (2011). We show that their estimator is a special case of the nonnegative LASSO, explaining its sparse nature observed in many applications. Recognizing this link, we extend the estimator, transforming it to a special case of the nonnegative elastic net. The extension improves the estimator's recovery of the true support and allows for more accurate estimates of the random coefficients' distribution. Our estimator is a generalization of the original estimator and therefore, is guaranteed to have a model fit at least as good as the original one. A theoretical analysis of both estimators' properties shows that, under conditions, our generalized estimator approximates the true distribution more accurately. Two Monte Carlo experiments and an application to a travel mode data set illustrate the improved performance of the generalized estimator.

Suggested Citation

  • Heiss, Florian & Hetzenecker, Stephan & Osterhaus, Maximilian, 2019. "Nonparametric estimation of the random coefficients model: An elastic net approach," DICE Discussion Papers 326, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
  • Handle: RePEc:zbw:dicedp:326
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/203671/1/1677378034.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bhat, Chandra R., 1998. "Accommodating variations in responsiveness to level-of-service measures in travel mode choice modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 495-507, September.
    2. Fox, Jeremy T. & Kim, Kyoo il & Yang, Chenyu, 2016. "A simple nonparametric approach to estimating the distribution of random coefficients in structural models," Journal of Econometrics, Elsevier, vol. 195(2), pages 236-254.
    3. Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan & Patrick Bajari, 2011. "A simple estimator for the distribution of random coefficients," Quantitative Economics, Econometric Society, vol. 2(3), pages 381-418, November.
    4. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    5. Sébastien Houde & Erica Myers, 2019. "Heterogeneous (Mis-) Perceptions of Energy Costs: Implications for Measurement and Policy Design," NBER Working Papers 25722, National Bureau of Economic Research, Inc.
    6. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    7. Aviv Nevo & John L. Turner & Jonathan W. Williams, 2016. "Usage‐Based Pricing and Demand for Residential Broadband," Econometrica, Econometric Society, vol. 84, pages 411-443, March.
    8. Wesley Blundell & Gautam Gowrisankaran & Ashley Langer, 2020. "Escalation of Scrutiny: The Gains from Dynamic Enforcement of Environmental Regulations," American Economic Review, American Economic Association, vol. 110(8), pages 2558-2585, August.
    9. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    10. Bhat, Chandra R., 1995. "A heteroscedastic extreme value model of intercity travel mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 471-483, December.
    11. Train, Kenneth, 2016. "Mixed logit with a flexible mixing distribution," Journal of choice modelling, Elsevier, vol. 19(C), pages 40-53.
    12. Hess, Stephane & Bierlaire, Michel & Polak, John W., 2005. "Estimation of value of travel-time savings using mixed logit models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(2-3), pages 221-236.
    13. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
    14. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    15. Bhat, Chandra R., 1997. "Covariance heterogeneity in nested logit models: Econometric structure and application to intercity travel," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 11-21, February.
    16. Chandra R. Bhat, 1997. "An Endogenous Segmentation Mode Choice Model with an Application to Intercity Travel," Transportation Science, INFORMS, vol. 31(1), pages 34-48, February.
    17. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    18. Wu, Lan & Yang, Yuehan & Liu, Hanzhong, 2014. "Nonnegative-lasso and application in index tracking," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 116-126.
    19. Gaston Illanes & Manisha Padi, 2019. "Competition, Asymmetric Information, and the Annuity Puzzle: Evidence from a Government-Run Exchange in Chile," Working Papers, Center for Retirement Research at Boston College wp2019-2, Center for Retirement Research.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Heiss, Florian & Hetzenecker, Stephan & Osterhaus, Maximilian, 2019. "Nonparametric estimation of the random coefficients model: An elastic net approach," Ruhr Economic Papers 824, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    2. Heiss, Florian & Hetzenecker, Stephan & Osterhaus, Maximilian, 2022. "Nonparametric estimation of the random coefficients model: An elastic net approach," Journal of Econometrics, Elsevier, vol. 229(2), pages 299-321.
    3. Rico Krueger & Akshay Vij & Taha H. Rashidi, 2018. "A Dirichlet Process Mixture Model of Discrete Choice," Papers 1801.06296, arXiv.org.
    4. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    5. Bansal, Prateek & Daziano, Ricardo A. & Achtnicht, Martin, 2018. "Comparison of parametric and semiparametric representations of unobserved preference heterogeneity in logit models," Journal of choice modelling, Elsevier, vol. 27(C), pages 97-113.
    6. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    7. Ke Wang & Chandra R. Bhat & Xin Ye, 2023. "A multinomial probit analysis of shanghai commute mode choice," Transportation, Springer, vol. 50(4), pages 1471-1495, August.
    8. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    9. Bansal, Prateek & Daziano, Ricardo A. & Achtnicht, Martin, 2018. "Extending the logit-mixed logit model for a combination of random and fixed parameters," Journal of choice modelling, Elsevier, vol. 27(C), pages 88-96.
    10. Zhang, Junyi & Kuwano, Masashi & Lee, Backjin & Fujiwara, Akimasa, 2009. "Modeling household discrete choice behavior incorporating heterogeneous group decision-making mechanisms," Transportation Research Part B: Methodological, Elsevier, vol. 43(2), pages 230-250, February.
    11. Bansal, Prateek & Daziano, Ricardo A & Guerra, Erick, 2018. "Minorization-Maximization (MM) algorithms for semiparametric logit models: Bottlenecks, extensions, and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 17-40.
    12. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
    13. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    14. Vij, Akshay & Krueger, Rico, 2017. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 76-101.
    15. Tien Mai & Patrick Jaillet, 2019. "Robust Product-line Pricing under Generalized Extreme Value Models," Papers 1912.09552, arXiv.org, revised Oct 2021.
    16. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
    17. Peter Davis & Pasquale Schiraldi, 2014. "The flexible coefficient multinomial logit (FC-MNL) model of demand for differentiated products," RAND Journal of Economics, RAND Corporation, vol. 45(1), pages 32-63, March.
    18. F Alpizar & F Carlsson & P Martinsson, 2003. "Using Choice Experiments for Non-Market Valuation," Economic Issues Journal Articles, Economic Issues, vol. 8(1), pages 83-110, March.
    19. Martin Burda & Remi Daviet, 2023. "Hamiltonian sequential Monte Carlo with application to consumer choice behavior," Econometric Reviews, Taylor & Francis Journals, vol. 42(1), pages 54-77, January.
    20. Isler, Cassiano Augusto & Blumenfeld, Marcelo & Caldeira, Gabriel Pereira & Roberts, Clive, 2024. "Long-Distance railway mode choice in Brazil: Evidence from a discrete choice experiment," Research in Transportation Economics, Elsevier, vol. 104(C).

    More about this item

    Keywords

    Random Coefficients; Mixed Logit; Nonparametric Estimation; Elastic Net;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • L - Industrial Organization

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:dicedp:326. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/diduede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.